Question

Factorize (a-b)3+(b-c)3+(c-a)3 by using only whole cube method

Answer 1

${x}^{3} + {y}^{3 } + {z}^{3} = 3xyz \: if \: x + y + z = 0$

therefore the answer is

$3(a - b)(b - c)(c - a) = 3a {b}^{2} + 3b {c}^{2} + 3 {a}^{2} c - 3 {a}^{2}b - 3a {c}^{2} - 3 {b}^{2} c$